Question

I -2 is a zero of the polynomial 3x²+2x+k find the value of k​

Answer 1

Answer:

p(x)=3x²+2x+k

x= -2 (given)

p(2)=3(2)²+2(2)+k

=> 12+4+k=0

=> 16+k=0

=> k=-16

hope it helps you....

Answer 2

Solution :

$\bf{\large{\underline{\bf{Given\::}}}}}$

If -2 is a zero of the polynomial 3x² + 2x + k.

$\bf{\large{\underline{\bf{To\:find\::}}}}}$

The value of k.

$\bf{\large{\underline{\bf{Explanation\::}}}}}$

Let the other zero be β

We have one zero is -2

We have polynomial p(x) = 3x² + 2x + k = 0

∴As we know that the quadratic polynomial compared with ax² + bx + c

• a = 3
• b = 2
• c = k

Now;

$\red{\underline{\underline{\bf{Sum\:of\:the\:zeroes\::}}}}}$

$\mapsto\sf{\alpha +\beta =\dfrac{-b}{a} =\dfrac{Coefficient\:of\:x}{Coefficient\:of\:x^{2} } }\\\\\\\mapsto\sf{-2+\beta =\dfrac{-2}{3} }\\\\\\\mapsto\sf{\beta =\dfrac{-2}{3} +2}\\\\\\\mapsto\sf{\beta =\dfrac{-2+6}{3} }\\\\\\\mapsto\sf{\pink{\beta =\dfrac{4}{3}...................(1) }}$

$\red{\underline{\underline{\bf{Product\:of\:the\:zeroes\::}}}}}$

$\mapsto\sf{\alpha \times \beta =\dfrac{c}{a} =\dfrac{Constant\:term}{Coefficient\:of\:x^{2} } }\\\\\\\mapsto\sf{-2\times \beta =\dfrac{k}{3} }\\\\\\\mapsto\sf{-2\beta =\dfrac{k}{3} }\\\\\\\mapsto\sf{k=-6\beta }\\\\\\\mapsto\sf{k=-\cancel{6}\times \dfrac{4}{\cancel{3}} \:\:\:\:\:[from(1)]}\\\\\\\mapsto\sf{k=-2\times 4}\\\\\\\mapsto\sf{\pink{k=-8}}$

Thus;

The value of k is -8 .